Dans cette thèse, nous abordons le problème de la planification de la production dans un système de type flow-shop, en tenant compte de l’aspect énergétique. Le système de production est composé de différentes machines fiables, séparées par des zones de stockage à capacité infinie. L’horizon de planification est composé de différentes périodes, chacune étant caractérisée par une durée, un coût d’électricité, une puissance maximale et des demandes de chaque produit. L’objectif consiste en la minimisation du coût total de production en terme d’électricité, stockage, mise marche (ou changement de série) et puissance demandée par période. Dans un premier temps, nous proposons une modélisation pour le problème de lot-sizing dans un système de type flow-shop, à capacité finie, dans le cas mono-produit. Étant donné que ce type de problème est NP-difficile, des méthodes approchées ont été développées afin de fournir des solutions de bonne qualité dans un temps réduit (heuristiques dédiées, heuristique de type Fix and Relax, algorithme génétique). Dans un deuxième temps, une généralisation du modèle pour le cas multi-produits a été considérée. De même, des méthodes approchées ont été proposées pour la résolution de ce type de problème / In this thesis, we deal with the production planning problem in a flow-shop system with energy consideration. The manufacturing system is composed of reliable machines separated by buffers with infinite capacities. The planning horizon is defined by a set of periods where each one is characterized by a length, an electricity price, a maximal allowed power and an external demand of each product. The purpose is to minimize the total production cost composed of electricity, inventory, set-up (or product series change) costs and a required power per period.In the first step, we propose mathematical models for a single item capacitated lot-sizing problem in a flow-shop system. Since this problem is known to be NP-hard, approximating methods are developed in order to provide solutions with good quality in a reasonable time (dedicated heuristics, Fix and Relax heuristic, genetic algorithm).In the second step, a generalization of the model for multi-items is considered. Similarly to the first case, approximating methods are proposed to solve this problem

Cette thèse a pour objectif la génération de séquences de franchissement dans les Réseaux de Petri Temporisés (RdPT) en utilisant une approche incrémentale. Le verrou principal auquel est confronté ce travail est l’explosion combinatoire qui résulte de la construction classique du graphe d’accessibilité du RdPT. Nous proposons d’utiliser la notion de séquence de steps temporisés, afin d’exprimer progressivement l’ensemble des séquences de franchissements permettant de passer d’un état courant à un état cible. La notion de step temporisé correspond à une abstraction logique du comportement du système considéré. Le caractère incrémental de l’approche a pour objectif de gagner en efficacité. En effet, il consiste à exprimer tout nouvel état de la résolution par rapport à une profondeur K+1, en fonction d’un état atteint à la profondeur K. Ainsi, nous proposons plusieurs algorithmes de recherche incrémentale permettant d'améliorer l'efficacité de la résolution des problèmes d'accessibilité. Nous utilisons ensuite la programmation par contraintes pour modéliser le problème de recherche d’accessibilité dans un RdPT et mettre en œuvre notre approche incrémentale. Notre approche permet également d’ajouter des contraintes spécifiques à un contexte de résolution. Nous avons notamment utilisé cette possibilité pour proposer des techniques d'identification des jetons dans un RdPT borné, dans le cadre de la reconfiguration des systèmes manufacturiers. Nous concluons par l’évaluation de différentes applications constituant des « benchmarks » permettant d’illustrer l'efficacité des approches proposées / This PhD thesis is dedicated to the generation of firing sequences in Timed Petri Net (TPN) using an incremental approach. To reduce the influence of the well-known combinatorial explosion issue, a unique sequence of timed steps is introduced to represent implicitly the underlying reachability graph of the TPN, without needing its whole construction. This sequence of timed steps is developed based on the logical abstraction technique. The advantage of the incremental approach is that it can express any state just from the last step information, instead of representing all states before.Several incremental search algorithms are introduced to improve the efficiency of our methodology. Constraint programming techniques are used to model and solve our incremental model, in which search strategies are developed that can search for solutions more efficiently. Our methodology can be used to add specific constraints to model realistic systems. Token identification techniques are developed to handle token confusion issues that appear when addressing the reconfiguration of manufacturing systems. Experimental benchmarks illustrate the effectiveness of approaches proposed in this thesis

Stochastic combinatorial optimization problems are combinatorial optimization problems where part of the problem data are probabilistic. The focus of this thesis is on stochastic routing problems, a class of stochastic combinatorial optimization problems that arise in distribution management. Stochastic routing problems involve finding the best solution to distribute goods across a logistic network. In the problems we tackle, we consider a setting in which the cost of a solution is described by a random variable; the goal is to find the solution that minimizes the expected cost. Solving such stochastic routing problems is a challenging task because of two main factors. First, the number of possible solutions grows exponentially with the instance size. Second, computing the expected cost of a solution is computationally very expensive. <p><br><p>To tackle stochastic routing problems, stochastic local search algorithms such as iterative improvement algorithms and metaheuristics are quite promising because they offer effective strategies to tackle the combinatorial nature of these problems. However, a crucial factor that determines the success of these algorithms in stochastic settings is the trade-off between the computation time needed to search for high quality solutions in a large search space and the computation time spent in computing the expected cost of solutions obtained during the search. <p><br><p>To compute the expected cost of solutions in stochastic routing problems, two classes of approaches have been proposed in the literature: analytical computation and empirical estimation. The former exactly computes the expected cost using closed-form expressions; the latter estimates the expected cost through Monte Carlo simulation.<p><br><p>Many previously proposed metaheuristics for stochastic routing problems use the analytical computation approach. However, in a large number of practical stochastic routing problems, due to the presence of complex constraints, the use of the analytical computation approach is difficult, time consuming or even impossible. Even for the prototypical stochastic routing problems that we consider in this thesis, the adoption of the analytical computation approach is computationally expensive. Notwithstanding the fact that the empirical estimation approach can address the issues posed by the analytical computation approach, its adoption in metaheuristics to tackle stochastic routing problems has never been thoroughly investigated. <p><br><p>In this thesis, we study two classical stochastic routing problems: the probabilistic traveling salesman problem (PTSP) and the vehicle routing problem with stochastic demands and customers (VRPSDC). The goal of the thesis is to design, implement, and analyze effective metaheuristics that use the empirical estimation approach to tackle these two problems. The main results of this thesis are: <p>1) The empirical estimation approach is a viable alternative to the widely-adopted analytical computation approach for the PTSP and the VRPSDC; <p>2) A principled adoption of the empirical estimation approach in metaheuristics results in high performing algorithms for tackling the PTSP and the VRPSDC. The estimation-based metaheuristics developed in this thesis for these two problems define the new state-of-the-art. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

In this thesis we focus on Stochastic combinatorial Optimization Problems (SCOPs), a wide class of combinatorial optimization problems under uncertainty, where part of the information about the problem data is unknown at the planning stage, but some knowledge about its probability distribution is assumed.<p><p>Optimization problems under uncertainty are complex and difficult, and often classical algorithmic approaches based on mathematical and dynamic programming are able to solve only very small problem instances. For this reason, in recent years metaheuristic algorithms such as Ant Colony Optimization, Evolutionary Computation, Simulated Annealing, Tabu Search and others, are emerging as successful alternatives to classical approaches.<p><p>In this thesis, metaheuristics that have been applied so far to SCOPs are introduced and the related literature is thoroughly reviewed. In particular, two properties of metaheuristics emerge from the survey: they are a valid alternative to exact classical methods for addressing real-sized SCOPs, and they are flexible, since they can be quite easily adapted to solve different SCOPs formulations, both static and dynamic. On the base of the current literature, we identify the following as the key open issues in solving SCOPs via metaheuristics: <p>(1) the design and integration of ad hoc, fast and effective objective function approximations inside the optimization algorithm;<p>(2) the estimation of the objective function by sampling when no closed-form expression for the objective function is available, and the study of methods to reduce the time complexity and noise inherent to this type of estimation;<p>(3) the characterization of the efficiency of metaheuristic variants with respect to different levels of stochasticity in the problem instances. <p><p>We investigate the above issues by focusing in particular on a SCOP belonging to the class of vehicle routing problems: the Probabilistic Traveling Salesman Problem (PTSP). For the PTSP, we consider the Ant Colony Optimization metaheuristic and we design efficient local search algorithms that can enhance its performance. We obtain state-of-the-art algorithms, but we show that they are effective only for instances above a certain level of stochasticity, otherwise it is more convenient to solve the problem as if it were deterministic.<p>The algorithmic variants based on an estimation of the objective function by sampling obtain worse results, but qualitatively have the same behavior of the algorithms based on the exact objective function, with respect to the level of stochasticity. Moreover, we show that the performance of algorithmic variants based on ad hoc approximations is strongly correlated with the absolute error of the approximation, and that the effect on local search of ad hoc approximations can be very degrading.<p><p>Finally, we briefly address another SCOP belonging to the class of vehicle routing problems: the Vehicle Routing Problem with Stochastic Demands (VRPSD). For this problem, we have implemented and tested several metaheuristics, and we have studied the impact of integrating in them different ad hoc approximations.<p> / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished

<p>A metaheuristic is a generic algorithmic template that, once properly instantiated, can be used for finding high quality solutions of combinatorial optimization problems.<p>For obtaining a fully functioning algorithm, a metaheuristic needs to be configured: typically some modules need to be instantiated and some parameters need to be tuned. For the sake of precision, we use the expression <em>parametric tuning</em> for referring to the tuning of numerical parameters, either continuous or discrete but in any case ordinal. <p>On the other hand, we use the expression <em>structural tuning</em> for referring to the problem of defining which modules should be included and, in general, to the problem of tuning parameters that are either boolean or categorical. Finally, with <em>tuning</em> we refer to the composite <em>structural and parametric tuning</em>.</p><p><p><p>Tuning metaheuristics is a very sensitive issue both in practical applications and in academic studies. Nevertheless, a precise definition of the tuning problem is missing in the literature. In this thesis, we argue that the problem of tuning a metaheuristic can be profitably described and solved as a machine learning problem.</p><p><p><p>Indeed, looking at the problem of tuning metaheuristics from a machine learning perspective, we are in the position of giving a formal statement of the tuning problem and to propose an algorithm, called F-Race, for tackling the problem itself. Moreover, always from this standpoint, we are able to highlight and discuss some catches and faults in the current research methodology in the metaheuristics field, and to propose some guidelines.</p><p><p><p>The thesis contains experimental results on the use of F-Race and some examples of practical applications. Among others, we present a feasibility study carried out by the German-based software company <em>SAP</em>, that concerned the possible use of F-Race for tuning a commercial computer program for vehicle routing and scheduling problems. Moreover, we discuss the successful use of F-Race for tuning the best performing algorithm submitted to the <em>International Timetabling Competition</em> organized in 2003 by the <em>Metaheuristics Network</em> and sponsored by <em>PATAT</em>, the international series of conferences on the <em>Practice and Theory of Automated Timetabling</em>.</p> / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished

Plusieurs problèmes d'optimisation combinatoire sont dits NP-difficiles et ne peuvent être résolus de façon optimale par des algorithmes exacts. Les métaheuristiques ont prouvé qu'elles pouvaient être efficaces pour résoudre un grand nombre de ces problèmes en leur trouvant des solutions approchées en un temps raisonnable. Cependant, face à des instances de grande taille, elles ont besoin d'un temps de calcul et d'une quantité d'espace mémoire considérables pour être performantes dans l'exploration de l'espace de recherche. Par conséquent, l'intérêt voué à leur déploiement sur des architectures de calcul haute performance a augmenté durant ces dernières années. Les approches de parallélisation existantes suivent généralement les paradigmes de passage de messages ou de mémoire partagée qui conviennent aux architectures traditionnelles à base de microprocesseurs, aussi appelés CPU (Central Processing Unit).Cependant, la recherche évolue très rapidement dans le domaine du parallélisme et de nouvelles architectures émergent, notamment les accélérateurs matériels qui permettent de décharger le CPU de certaines de ses tâches. Parmi ceux-ci, les processeurs graphiques ou GPU (Graphics Processing Units) présentent une architecture massivement parallèle possédant un grand potentiel mais aussi de nouvelles difficultés d'algorithmique et de programmation. En effet, les modèles de parallélisation de métaheuristiques existants sont généralement inadaptés aux environnements de calcul de type GPU. Certains travaux ont d'ailleurs abordé ce sujet sans toutefois y apporter une vision globale et fondamentale.L'objectif général de cette thèse est de proposer un cadre de référence permettant l'implémentation efficace des métaheuristiques sur des architectures parallèles basées sur les GPU. Elle débute par un état de l'art décrivant les travaux existants sur la parallélisation GPU des métaheuristiques et les classifications générales des métaheuristiques parallèles. Une taxonomie originale est ensuite proposée afin de classifier les implémentations recensées et de formaliser les stratégies de parallélisation sur GPU dans un cadre méthodologique cohérent. Cette thèse vise également à valider cette taxonomie en exploitant ses principales composantes pour proposer des stratégies de parallélisation originales spécifiquement adaptées aux architectures GPU. Plusieurs implémentations performantes basées sur les métaheuristiques d'Optimisation par Colonie de Fourmis et de Recherche Locale Itérée sont ainsi proposées pour la résolution du problème du Voyageur de Commerce. Une étude expérimentale structurée et minutieuse est réalisée afin d'évaluer et de comparer la performance des approches autant au niveau de la qualité des solutions trouvées que de la réduction du temps de calcul. / Several combinatorial optimization problems are NP-hard and can only be solved optimally by exact algorithms for small instances. Metaheuristics have proved to be effective in solving many of these problems by finding approximate solutions in a reasonable time. However, dealing with large instances, they may require considerable computation time and amount of memory space to be efficient in the exploration of the search space. Therefore, the interest devoted to their deployment on high performance computing architectures has increased over the past years. Existing parallelization approaches generally follow the message-passing and shared-memory computing paradigms which are suitable for traditional architectures based on microprocessors, also called CPU (Central Processing Unit). However, research in the field of parallel computing is rapidly evolving and new architectures emerge, including hardware accelerators which offloads the CPU of some of its tasks. Among them, graphics processors or GPUs (Graphics Processing Units) have a massively parallel architecture with great potential but also imply new algorithmic and programming challenges. In fact, existing parallelization models of metaheuristics are generally unsuited to computing environments like GPUs. Few works have tackled this subject without providing a comprehensive and fundamental view of it.The general purpose of this thesis is to propose a framework for the effective implementation of metaheuristics on parallel architectures based on GPUs. It begins with a state of the art describing existing works on GPU parallelization of metaheuristics and general classifications of parallel metaheuristics. An original taxonomy is then designed to classify identified implementations and to formalize GPU parallelization strategies in a coherent methodological framework. This thesis also aims to validate this taxonomy by exploiting its main components to propose original parallelization strategies specifically tailored to GPU architectures. Several effective implementations based on Ant Colony Optimization and Iterated Local Search metaheuristics are thus proposed for solving the Travelling Salesman Problem. A structured and thorough experimental study is conducted to evaluate and compare the performance of approaches on criteria related to solution quality and computing time reduction.

Nous nous intéressons dans cette thèse à la problématique de la décision collective. L’objectif est de déterminer une solution de compromis pour des problèmes soumis à de multiples points de vue. Les problèmes considérés sont de nature combinatoire. Plus précisément, il s’agit de la classe des systèmes d’ensembles qui ont une structure de matroïde. La théorie des matroïdes est centrale en optimisation combinatoire, elle a permis d’unifier des structures apparemment séparées comme les arbres et les couplages dans les graphes et elle a engendré des algorithmes efficaces pour résoudre des problèmes d’optimisation non triviaux en temps polynomial. Nous nous intéressons à fournir des algorithmes d’approximation polynomiaux centralisés et décentralisés avec garantie de performance pour déterminer une solution de compromis qui est une base du matroïde. La solution de compromis doit également être équitable pour tous les membres de la collectivité. Nous portons un intérêt particulier au problème de partage équitable de biens indivisibles qui est une thématique importante en choix social computationnel et dont le problème se modélise par les matroïdes. / In this thesis, we are interested in collective decision-making. The objective is to find a tradeoff solution for problems that are evaluated by multiple points of view. We consider problems having a matroid structure. Matroid theory is significant in combinatorial optimization, it helped to unify apparently separated structures like forests and matchings in graphs and it includes efficient algorithms for solving non-trivial optimization problems in polynomial time. We are interested to provide polynomial time centralized and decentralized approximation algorithms for finding a tradeoff solution which is a base of the matroid. The tradeoff solution must also be fair for all the members of the community. We are particularly interested in the issue of the fair division of indivisible goods which is central in computational social choice and that can be modeled by matroids.

Vehicle Routing Problem with Time Windows is a hard optimization problem. Even though it has numerous practical applications, the question of solving it efficiently has not been satisfyingly solved yet. This thesis studies the Vehicle Routing Problem with Time Windows and presents several new algorithms for solving it. There are two heuristics presented here, as well as several more complex algorithms which use those heuristics as their components. The efficiency of presented techniques is evaluated experimentally using a set of test samples. As a part of this thesis, I have also developed a desktop application which implements presented algorithms and provides a few additional features useful for solving routing prob-lems in practice. Among others, there is a generator of pseudo-random problem instances and several visualization methods.

Un système de systèmes est un système dont les composants sont eux-mêmes des systèmes indépendants, tous communiquant pour atteindre un objectif commun. Lorsque ces systèmes sont mobiles, il peut être difficile d'établir des connexions de bout-en-bout. L'architecture mise en place dans de telles situations est appelée réseau tolérant aux délais. Les données sont transmises d'un système à l'autre – selon les opportunités de communication, appelées contacts, qui apparaissent lorsque deux systèmes sont proches – et disséminées dans l'ensemble du réseau avec l'espoir que chaque message atteigne sa destination. Si une donnée est trop volumineuse, elle est découpée. Chaque fragment est alors transmis séparément.Nous supposons ici que la séquence des contacts est connue. On s'intéresse donc à des applications où la mobilité des systèmes est prédictible (les réseaux de satellites par exemple). Nous cherchons à exploiter cette connaissance pour acheminer efficacement des informations depuis leurs sources jusqu'à leurs destinataires. Nous devons répondre à la question : « Quels éléments de données doivent être transférés lors de chaque contact pour minimiser le temps de dissémination » ?Nous formalisons tout d'abord ce problème, appelé problème de dissémination, et montrons qu'il est NP-difficile au sens fort. Nous proposons ensuite des algorithmes pour le résoudre. Ces derniers reposent sur des règles de dominance, des procédures de prétraitement, la programmation linéaire en nombres entiers, et la programmation par contraintes. Une partie est dédiée à la recherche de solutions robustes. Enfin, nous rapportons des résultats numériques montrant l'efficacité de nos algorithmes. / Systems of systems are supersystems comprising elements which are themselves independent operational systems, all interacting to achieve a common goal. When the subsystems are mobile, these may suffer from a lack of continuous end-to-end connectivity. To address the technical issues in such networks, the common approach is termed delay-tolerant networking. Routing relies on a store-forward mechanism. Data are sent from one system to another – depending on the communication opportunities, termed contacts, that arise when two systems are close – and stored throughout the network in hope that all messages will reach their destination. If data are too large, these must be split. Each fragment is then transmitted separately.In this work, we assume that the sequence of contacts is known. Thus, we focus on applications where it is possible to make realistic predictions about system mobility (e.g. satellite networks). We study the problem of making the best use of knowledge about possibilities for communication when data need to be routed from a set of systems to another within a given time horizon. The fundamental question is: "Which elements of the information should be transferred during each contact so that the dissemination length is minimized"?We first formalize the so-called dissemination problem, and prove this is strongly NP-Hard. We then propose algorithms to solve it. These relies on different dominance rules, preprocessing procedures, integer-linear programming, and constraint programming. A chapter is dedicated to the search for robust solutions. Finally experimental results are reported to show the efficiency of our algorithms in practice.

Dans cette thèse, nous nous sommes intéressés à la résolution approchée de problèmes de tournées de véhicules. Nous avons exploité des travaux menés sur les graphes d'intervalles et des propriétés de dominance relatives aux tournées saturées pour traiter les problèmes de tournées sélectives plus efficacement. Des approches basées sur un algorithme d'optimisation par essaim particulaire et un algorithme mémétique ont été proposées. Les métaheuristiques développées font appel à un ensemble de techniques particulièrement efficaces telles que le découpage optimal, les opérateurs de croisement génétiques ainsi que des méthodes de recherches locales. Nous nous sommes intéressés également aux problèmes de tournées classiques avec fenêtres de temps. Différents prétraitements ont été introduits pour obtenir des bornes inférieures sur le nombre de véhicules. Ces prétraitements s'inspirent de méthodes issues de modèles de graphes, de problème d'ordonnancement et de problèmes de bin packing avec conflits. Nous avons montré également l'utilité des méthodes développées dans un contexte industriel à travers la réalisation d'un portail de services mobilité. / In this thesis, we focused on the development of heuristic approaches for solvingvehicle routing problems. We exploited researches conducted on interval graphsand dominance properties of saturated tours to deal more efficiently with selectivevehicle routing problems. An adaptation of a particle swarm optimization algorithmand a memetic algorithm is proposed. The metaheuristics that we developed arebased on effective techniques such as optimal split, genetic crossover operatorsand local searches. We are also interested in classical vehicle problems with timewindows. Various pre-processing methods are introduced to obtain lower boundson the number of vehicles. These methods are based on many approaches usinggraph models, scheduling problems and bin packing problems with conflicts. Wealso showed the effectiveness of the developed methods with an industrial applicationby implementing a portal of mobility services.